So sánh \(A=\dfrac{13^{19}+1}{13^{18}+1}\) và \(B=\dfrac{13^{20}+1}{13^{19}+1}\)
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12 tháng 9 2023
a) \(\dfrac{17}{20}< \dfrac{18}{20}< \dfrac{18}{19}\Rightarrow\dfrac{17}{20}< \dfrac{18}{19}\)
b) \(\dfrac{19}{18}>\dfrac{19+2024}{18+2024}=\dfrac{2023}{2022}\Rightarrow\dfrac{19}{18}>\dfrac{2023}{2022}\)
c) \(\dfrac{135}{175}=\dfrac{27}{35}\)
\(\dfrac{13}{17}=\dfrac{26}{34}< \dfrac{26+1}{34+1}=\dfrac{27}{35}\)
\(\Rightarrow\dfrac{13}{17}< \dfrac{135}{175}\)
28 tháng 2 2018
Ta có :
\(\dfrac{1}{11}>\dfrac{1}{20}\\ \dfrac{1}{12}>\dfrac{1}{20}\\ ..........\\ \dfrac{1}{20}=\dfrac{1}{20}\)
\(\Rightarrow\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{20}>\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}\\ \Rightarrow S>\dfrac{10}{20}\\ \Rightarrow S>\dfrac{1}{2}\)
SB
9 tháng 6 2021
quy đồng
lấy 36 làm mẫu số chung
-13 / 12 = -39/36
-19/18 = -38/36
mà đối với số dương số nào lớn hơn thì số đó bé hơn
vậy -39/36 <-38/36
=> -13 / 12 < -19/18 = -38/36
10 tháng 6 2021
Giải:
\(\dfrac{-13}{12}=-1+\dfrac{-1}{12}\)
\(\dfrac{-19}{18}=-1+\dfrac{-1}{18}\)
Vì \(\dfrac{-1}{12}< \dfrac{-1}{18}\) nên \(\dfrac{-13}{12}< \dfrac{-19}{18}\)
Chúc bạn học tốt!
26 tháng 2 2022
a, \(\dfrac{14}{13}-\dfrac{1}{13}-\dfrac{19}{20}=1-\dfrac{19}{20}=\dfrac{1}{20}\)
b, \(-\dfrac{24}{17}+\dfrac{7}{17}+\dfrac{1}{16}=\dfrac{-17}{17}+\dfrac{1}{16}=-1+\dfrac{1}{16}=-\dfrac{15}{16}\)
29 tháng 4 2015
Vì 1320+1/1319+1>1
=>1320+1/1319+1>1320+1+12/1319+1+12
Ta có: 1320+1+12/1319+12
= 1320+13/1319+13
=13(1319+1)/13(1318+1)
= 1319+1/1318+1
=> 1320+1/1319+1> 1319+1/1318+1
Vậy A<B
29 tháng 4 2015
\(B=\frac{13^{20}+1}{13^{19}+1}>1\)
\(B=\frac{13^{20}+1}{13^{19}+1}>\frac{13^{20}+1+12}{13^{19}+1+12}\)
\(B=\frac{13^{20}+13}{13^{19}+13}=\frac{13\left(13^{19}+1\right)}{13\left(13^{18}+1\right)}\)
\(B=\frac{13^{19}+1}{13^{18}+1}=A\)
\(\Rightarrow B>A\)
SN
2
TV
3
TT
28 tháng 4 2021
\(ta có A=\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{15}}{13^{16}}+1\)=\(\dfrac{1}{13}+1\)
B=\(\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{16}}{13^{17}}+1\)=\(\dfrac{1}{13}+1\)
vậy A=B
2 tháng 5 2017
Ta có:\(\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{16}>4\cdot\dfrac{1}{16}=\dfrac{1}{4}\)
\(\dfrac{1}{17}+\dfrac{1}{18}+\dfrac{1}{19}+\dfrac{1}{20}>4\cdot\dfrac{1}{20}=\dfrac{1}{5}\)
=>\(\dfrac{1}{13}+\dfrac{1}{14}+...+\dfrac{1}{20}>\dfrac{1}{4}+\dfrac{1}{5}=\dfrac{9}{20}\)
=>A>\(\dfrac{1}{12}+\dfrac{9}{20}\)
\(\dfrac{1}{12}>\dfrac{1}{20}\)
=>\(A>\dfrac{1}{20}+\dfrac{9}{20}=\dfrac{1}{2}\)
Vậy...
\(\dfrac{1}{13}A=\dfrac{13^{19}+1}{13^{19}+\dfrac{1}{13}}=1+\dfrac{\dfrac{12}{13}}{13^{19}+\dfrac{1}{13}}\)
\(\dfrac{1}{13}B=\dfrac{13^{20}+1}{13^{20}+\dfrac{1}{13}}=1+\dfrac{\dfrac{12}{13}}{13^{20}+\dfrac{1}{13}}\)
Vì \(\dfrac{\dfrac{12}{13}}{13^{20}+\dfrac{1}{13}}< \dfrac{\dfrac{12}{13}}{13^{20}+\dfrac{1}{13}}\Rightarrow1+\dfrac{\dfrac{12}{13}}{13^{20}+\dfrac{1}{13}}< 1+\dfrac{\dfrac{12}{13}}{13^{20}+\dfrac{1}{13}}\)
\(\Rightarrow\dfrac{1}{13}A>\dfrac{1}{13}B\Rightarrow A>B\)
Vậy...
Ta xét hiệu:
\(A-1=\dfrac{3^{19}+1}{3^{18}+1}-1=\dfrac{3^{19}-3^{18}}{3^{18}+1}=\dfrac{3^{18}.2}{3^{18}+1}\)
\(B-1=\dfrac{3^{20}+1}{3^{19}+1}-1=\dfrac{3^{20}-3^{19}}{3^{19}+1}=\dfrac{3^{19}.2}{3^{19}+1}\)
Xét: \(\dfrac{A-1}{B-1}=\dfrac{3^{18}.2}{3^{18}+1}\cdot\dfrac{3^{19}+1}{3^{19}.2}=\dfrac{3^{19}+1}{\left(3^{18}+1\right).3}=\dfrac{3^{19}+1}{3^{19}+3}< 1\)
=> A-1<B-1
=>A<B